Electromechanical calculating apparatus



Jan. 13, 1953 G. AGINS 2,625,327

ELECTROMECHANICAL CALCULATING APPARATUS Filed Dec. 4, 1945 3 Sheets-Sheet 1 U51 I Z1 mu I AW; 770/? 5K5- Jan. 13, 1953 G. AGINS 2,625,327

ELECTROMECHANICAL CALCULATING APPARATUS Filed Dec. 4, 1945 Sheets-Sheet 2 (ZECflQ/Ml.)

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6a acre/614 ira/e a INVENTOR' G eorge Agi'rw Jan. 13, 1953 AGlNs 2,625,327

ELECTROMECHANICAL CALCULATING APPARATUS Filed Dec. 4, 1945 3' Sheets-Sheet 3- lhlll "Hi" hill": m! n Fig. 6 BY V George Aslns Patented Jan. 13, 1953 ELECTROMECHANICAL CALCULATING APPARATUS George Agins, Brooklyn, N. Y., asslgnor to Arms. Corporation, Brooklyn, N. Y., a corporation of New York Application December 4, 1945, Serial No. 632,651

Claims. (01. 235-61) This invention relates to electromechanical calculating apparatus, and has particular reference to an improved device for multiplying and ratio work generally.

One form of electromechanical calculating apparatus of the general type to which the present invention pertains is disclosed in copending application Serial No. 346,183, filed July 18, 1940, by applicant, refiled December 6, 1946, as a continuation, and issued March 29, 1949, as Patent No. 2,465,624. By means of that apparatus, various trigonometric functions of a variable angle can be continuously produced and simultaneously multiplied by a linear value. In that apparatus the linear value, in the form of a modulation of a carrier frequency, is fed into a stator winding and, the angle value is applied to a rotor winding in the field of the stator winding, whereby the answer appears across the output rotor winding as an electrical value. Such a device has proven eminently satisfactory for making trigonometric calculations involving vectors. However, it is de-. sirable in certain computations to be able to multiply a value furnished as a. modulation of a carrier frequency by the angle value directly, rather than by a trigonometric function of the angle. It is also sometimes desirable to use such a device for multiplying two continuously varying values by each other, one of them being applied to the device as an amplitude modulation of a carrier frequency and the other applied as an angle, and it is to this latter use that this invention is especially directed.

In accordance with the invention, when a. trig-onometric multiplier, such as described in said copending application, is reconstructed to provide certain coils connected in series in a certain position and of a certain number of winding turns relatively to the winding turns of the other coils of the multiplier, the output voltage over a considerable angle of the rotary shaft input is substantially directly proportional to the angle, and therefore the device becomes a proportionality machine or multiplier. For instance, if the stat-or or modulation member is provided with one coil and the rotor or angle member has two coils arranged in quadrature. one in series with the stator coil, this eflect obtains. Alternatively, if the stator member has two coils in quadrature and the rotor has one coil with the series connection, the eifects are similar, provided, of course, that in each case the turn ratios of all the coils are fixed in a certain way, as hereinafter specified.

It will be seen that the electromechanical calculating apparatus of this invention smoothly and accurately functions as a proportionality unit, or a multiplier, directly producing an electrical value without the step-by-step action that son of a step variation anywhere in its circuit.

A more complete understanding of the invention may be had by reference to the accompanying drawings, in which:

Figure 1 is an electrical diagram of one form of the electromechanical calculating apparatus of this invention;

Fig. 2 is an electrical diagram of a modification of the invention;

Fig. 3 is a wave diagram of the electrical output of the apparatus of this invention;

Fig. 4 illustrates a physical embodiment of the theoretical arrangement of Fig. 1;

Fig. 5 shows a similar physical embodiment of the arrangement of Fig. 2; and,

Fig. 6 is an axial section through an apparatus embodying this invention adapted for quantity manufacture.

Referring to Fig. 1, the winding I 0 represents a stator coil in an electromechanical calculating apparatus or resolver embodying this invention, and the windings II and I2 represent similar coils arranged in space quadrature and serving as the corresponding rotor which is adapted to be rotated in the field of stator III by angle input shaft I3. In the form of the invention shown in Fig. 1, the stator winding I 0 is the input winding to which is applied an alternating current modulated as to amplitude with a numerical value, which is one factor of the multiplication to be performed. Such modulation may be prepared by the potentiometer or voltage divider l4,

} wherein the rotary shaft I5 drives a brush I6 over a-uni-form resistance coil II, so as to modulate the alternating current applied to coil II by the source I8, as is well understood. Also as shown in Fig. 1, the stator winding I0 is connected to output terminals 20 of potentiometer I 4 and rotor winding II is connected in series with stator winding III by flexible leads IS. The other rotor winding I2 is connected by flexible leads to the terminals of a suitable indicator such as the meter 22, to be described.

In operation of the electromechanical calculating apparatus of this invention as shown in Fig. 1, the alternating current from source I8 is modulated in potentiometer It by the adjustment .quency current across output terminals vIii of potentiometer I4 is fed to coil l and the magnetic field created thereby aflects, by electromagnetic induction, the two rotor coils H and ii in that held so as t produce therein currents proportional to the modulation value and a sine or cosine of the angle, 9, through which they are rotated by shaft l3 relatively to the stator coil In. However, inasmuch as the rotor coil H is connected in series with the stator coil III, the modulated current in. coil in flows also in the rotor coil ll. threading the coil in is not that which would be produced solely by the stator coil Ill, but is also a function of the angle 0, the input angle which rotor coil ll makes with the stator coil Ill. The rotor coil l2, which is the product or output coil. therefore rotates through the input angle 0 in a field which in turn is being modified by a function of the same angle, as is hereinafter set forth mathematically. As a result of this arrangement, it will be seen that. for a very considerable portion of its total possible rotation, rotor coil l2 will give as its output the product of the modulation value applied to coils l0 and II and the rotor angle 0. This highly accurate Thus, the magnetic field 7 product, AB, may be represented by the deflection of the pointer or scale index of the meter 22, for example.

According to Esbachs Handbook of Engineering Fundamentals," published in 1936 by John Wiley 8: Son, section 8, page 29, formula (24), if two coils like in and II in Fig. l have mutual inductance M, resistances 1'1 and r2, inductances L1 and In, currents i1 and i: and rates of change of currents di, dz, a and 7s and consequent voltage drops in and 02, then where a=reluctance of the system. Substitut- 1118 (5) in (3) and (4) p e =aNfigg+aN Nz z cos 0 (6) But, since coils l0 and II are in series the total voltage 4 e=e +e =ag;(N +2N N cos 0+N,*) (8) Now, if e =output voltage (product), and N== turns in coil i2, then d c =N sin d=agN N sin 0 (9) substituting for a p E d! the value e I N,=+' 21ml, cos 0+N (8) I: eN;N; Bill 9 N,=+2N' M75 0'? N? 8 N1N3 Sin (11) C N1 +N: 1+k cos 0 where k 2N N N1+Ni I1 k=.52, then Y is seen to be linear to within 133% between 1-45",

or the points 23 and 24 on the curve of Fig. 3, in which the horizontal or abscissa axis represents the input angle for the function 0, and the ordinates are corresponding products representing A0, assuming factor A to remain constant. As is evident, the semi-circle at the left of Fig. 3 represents the circular path of the rotor coil H. The transformation ratio N1 which results in a vlaue of 'k=.52 can be found from the relationship between k, N1, and N: given above. Thus:

ZZAL l 52 2( )+.52 0

from which is found to be either .28 or 3.57.

The calculating apparatus of this invention accordingly diifers advantageously for the stated purposes from that of the trigonometric resolver disclosed in the said copending application whose characteristic output curve is shown by the solid line curve in Fig. 3, which has a characteristic sine form with the slight symmetrical bulges between points 23 and 24 at 315 and 45. Compared to this curve, the output curve of the apparatus of the present invention is straight Lb etween the 45 and 135 positions of the rotor, as indicated by the dotted-line between points 23 and 24 in Fig. 3. The apparatus of this invention accordingly functions as a proportionality unit or multiplier, but unlike the step-bystep action of a multiplier of the voltage divider type like that indicated at H, the action of the apparatus of the invention is perfectly smooth, the steps in changing output being infinitesimal. This is advantageous for use in calculatin mechanisms where the action is regenerative, because such a system is easily thrown into oscillation by step variation anywhere in the circuit.

In order to avoid phase shift through the multiplier and consequent error, the output rotor coil J2 must be so placed relatively to the other rotor coil ii that there is practically no mutual inductance at any time.

Referring to the modification of the invention shown by Fig. 2, the same coils are used as indicated by the same reference characters and the stator coil in is in series with the rotor coil II as seen in Fig. 1. However, the coil l2 has been'removed from the rotor and placed on the stator at right angles to the stator coil It, as shown at I2a, so that stator coils Ill and Ho shall have substantially no mutual inductance. With this arrangement the same formulas and curves obtain with appropriate modification, and the product of the input factors A and is shown by measurement of the output voltage of coil l2a, as on the meter 22. Thus, instead of obtaining the product voltage from one rotor coil as in Fig. 1, it may be obtained from a single stator coil 12a in Fig. 2, and the formula corresponding here to aforementioned formula (11) will be e"=instantaneous voltage of coil l'2a, N4=number of turns of coil 12a.

This arrangement also has the advantage of eliminating one pair of slip-rings, which is especially valuable in computer work.

Referring to Fig. 4, which is a transverse section through an electromechanical physical embodiment of the calculating apparatus shown diagrammatically in Fig. 1, and also to Fig. 6, which is an axial section through the same arrangement, adapted for quantity production, the same reference characters being used to designate the parts corresponding to those of Fig. l. The stator poles comprise a stack of laminations of iron, soft steel, or equivalent magnetic material mounted on or constituting part of a suitable conducting frame 26 having end plates 21 in which the rotor shaft I3 is suitably journalled, as shown in Fig. 6. Shaft l3 carries a laminated core 28 which is slotted to form poles 29 cooperating across an air gap 30 with the stator poles 25 and carrying the rotor windings II and [2 as shown.

Input of the electrical factor A is supplied from terminals 20 to stator coils It and by wires iii to rotor coils II, as by the slip-rings, brushes 3| and connection 32 shown in Fig. 6. Although only one brush and slip-ring combination is necessary, two sets are shown, the dotted line brush being omitted if desired, by using the arrangement of Fig. 2. Input of the mechanical angle factor 0 on rotor shaft l3 causes the electrical product A0 to be induced in coil l2 and is taken ofi by connection 33 and slip-ring and brush combinations 34 and impressed on terminals 2| of a meter or other indicator 22, as shown in Fig. 1. The slip-rings may be carried on an insulating extension 35 on shaft l3 and housed with brushes 3i and 34 in an insulatin housing 36 mounted on casing 26 and also servmg as a brush holder as shown in Fig. 6, which illustrates an assembly suitable for quantity production.

Just as the mechanical arrangement of Fig. 4 follows the schematic arrangement of Fig. 1, the mechanical arrangement of Fig. 5 follows the schematic arrangement of Fig. 2. Thus, the same parts in Figs. 2 and 5 are identified by the same reference characters, coils i2a forming with coils ill of the stator coilsof the assembly and the rotor coils ll mounted on mechanical factor 0 input shaft 13 as before. Fig. 6 will serve to illustrate a perferred embodiment of the arrangement of Fig. 5 as well as that of Fig. 4, except that the stator includes two coils, in and Ma and the rotor one coil, ll, instead of two. The operation of Fig. 5 is the same as that described in connection with Fi 2.

Although certain preferrred embodiments of the invention have been illustrated and described herein, it is to be understood that the invention is not limited thereby, but is susceptible of changes in form and detail within the scope of the appended claims.

I claim:

1. In an electromechanical calculating apparatus for computing the product of-two values, the combination of an input stator winding, a source of input alternating current connected theret for creating a magnetic'field therewith, said source being adjustable in accordance with the magnitude of one of said values, an input rotor winding inductively positioned in the magnetic field of said input stator winding, mechanical input means for adjusting the angle of said rotor winding relatively to said stator winding in accordance with the other of said values, series connections between said rotor winding and said stator winding, an output winding positioned in inductive relation to one of said input stator and rotor windings and responsive only to a function of the magnetic fields created thereby, and indicating means directly connected to said output winding for indicating the product of said values, the turn ratio between said input rotor winding and said input stator winding being substantially .28 or 3.57.

2. In an electromechanical calculating apparatus for computing the product of two values, the combination of an input stator winding, a source of input alternating current connected thereto for creating a magnetic field therewith, said source being adiustable in accordance with the magnitude of one of said values, an input rotor winding inductively positioned in the magnetic field of said input stator winding, mechanical input means for adjusting the angle of said rotor winding relatively to said stator winding in accordance with the other of said values, series connections between said rotor windings and said stator winding, an output stator winding arranged in space quadrature to said input stator winding and positioned in inductive relation to said input rotor winding, said output stator winding being responsive only to afunction of the A magnetic fields created by said input stator and rotor windings, and indicating means directly connected to said output winding for indicating the product of said two values, the turn ratio between said input rotor winding and said input stator winding being substantially .28 or 3.57.

3. In an electromechanical calculating apparatus for computing the product of two values, the combination of an input stator winding. a

source of input alternating current connected thereto for creating a magnetic field therewith, said source being adjustable in accordance with the magnitude of one of said values, an input rotor winding inductively positioned in the magnetic field 01' said input stator winding, mechanical input means for adjusting the angle of said rotor winding relatively to said stator winding in accordance with the other of said values, series connections between said rotor winding and saidstator winding, an output rotor winding connected to said mechanical input means and arranged in space-quadrature to said input rotor winding, said output rotor winding being responsive only to a function of the magnetic fields created by said input stator and rotor windings, and indicating means directly connected to said output winding for indicating the product of said two values, the turn ratio between said input rotor winding and said input stator winding being substantially .28 or 3:57,

4. In an electromechanical calculating apparatus for computing the product of two values, the combination of an input stator winding, a source of input alternating current connected thereto for creating a magnetic field therewith, means interposed between said source and said input stator winding for modulating the alternating current fed to the former in accordance with the magnitude of one of said values, an input rotor winding inductively positioned in the magnetic field of said input stator winding, mechanical input means for adjusting the angle of said rotor winding relatively to said stator winding in accordance with the other of said values, series connections between said rotor winding and said stator winding, an output stator winding arranged in space quadrature to said input stator winding and positioned in inductive relation to said input rotor winding, said output stator winding being responsive only to a function of the magnetic fields created by said input stator and rotor windings, and indicating means connected to said output winding for indicating the product of said two values, the turn ratio between said input rotor winding and said input stator winding being substantially .28 or 3.57.

5. In an electromechanical calculating apparatus for computing the product of two values, the combination of an input stator winding, a

source of input alternating current connected thereto for creating a magentic field therewith,-

means interposed between said source and said input stator winding for modulating the alternating current fed to the former in accordance with the magnitude of one of said values, an input rotor winding inductively positioned in the magnetic field of said input stator winding, mechanical input means for adjusting the angle of said rotor winding relatively to said stator winding in accordance with the other of said values, series connections between said rotor winding and said stator winding, an output rotor winding connected to said mechanical input means and arranged in space quadrature to said input rotor winding, said output rotor winding being responsive only to a function of the magnetic fields created by said input stator and input rotor windings, and indicating means connected to said output winding for indicating the product of said two values, the turn ratio between said input rotor winding and said input stator winding being substantially .28 or 3.57.

6. In an electromechanical calculating apparathe combination of an input stator winding having N1 turns, a source 01 input alternating current connected thereto for creating a magnetic field therewith, a potentiometer interposed between said source and said input stator winding and having a coil and a brush adjustable there over, mechanical input means for adjusting said brush in accordance with the magnitude of one of said values to thereby modulate the alternating current fed to said input stator winding, an input rotor winding of N: turns inductively positioned in the magnetic field of said input stator winding, mechanical input means for ad justing the angle of saidrotor winding relatively to said stator winding in accordance with the other of said values, series connections betweensaid rotor winding and said stator winding, an output stator winding positioned in space quadrature to said input stator winding and responsive only to a function 01 the magnetic fields created by said input stator and input rotor windings, and indicating means connected to said output winding for indicating the product of said two values, said input stator winding and said input rotor winding being so designed that the value for the quantity is substantially .28 or 3.57 while the value for the quantity 2N N3 N1 +N2 is substantially .52.

7. In an electromechanical calculating apparatus for computing the product of two values, the combination of an input stator winding having N1 turns, a source of input alternating current connected thereto for creating a magnetic field therewith, a potentiometer interposed between said source and said input stator winding and having a coil and a brush adjustable thereover, mechanical input means for adjusting said brush in accordance with the magnitude of one of said values to thereby modulate the alternating current fed to said input stator winding, an input rotor winding of N2 turns inductively positioned in the magnetic field of said input stator winding, mechanical input means for adjusting the angle of said rotor winding relatively to said stator winding in accordance with the other of said values, series connections between said rotor winding and said stator winding, an output rotor winding connected to said mechanical input means and arranged in space quadrature to said input rotor winding, said output rotor winding being responsive only to a function of the magnetic fields created by said input stator and input rotor windings, and indicating means connected to said output winding for indicating the product of said two values, said input stator winding and said input rotor winding being so designed that the value for the quantity N1 7 is substantially .28 or 3.57 while the value for the quantity is substantially .52.

8. In an-electromechanical calculating apparatus for computing the products of two values, 7 tus for multiplying a variable value represented by modulation of a first carrier wave continuously by a second variable represented by an angle and expressing the product as a modulation 0! a similar carrier wave, the combination of a source of said first carrier wave, means for modulating said carrier wave in accordance with said variable value, an induction member connected to said source for creating a magnetic field in response to said first modulated carrier wave, a second induction member sitioned in said magnetic field, means for adjusting said second induction member through said angle, series connections between said first and second induction members, a third induction member positioned in inductive relation to one of said first and second induction members and responsive only to a function-oi the magnetic fields created by said first and second induction members, and an indicator energized by the voltage induced in said third member for indicating said multiplication, the turn ratio between said second and first induction members being substantially .28 or 9. In an electromechanical calculating apparatus for multiplying a variable value represented by modulation of a first carrier w'ave continuously by said second variable represented by an angle and expressing the product as a modulation of a similar carrier wave, the combination oi a source, of said first carrier wave, means for modulating said carrier wave in accordance with the magnitude of said variable value, an induction member connected to said source for creating a magnetic field in response to said first modulated carrier wave, a. second induction member positioned in said magnetic field, means for adiusting said second induction memberthrough said angle, series connections between said first and second induction members, a third induction member inthe field or said first induction member and responsive only to the magnetic fields created by said first and second induction members, and an indicator energized by the voltage induced in said third member for in dicating said multiplication, the turn ratio between said second and first induction members being substantially .28 or 3.57.

10. In an electromechanical calculating apparatus tor multiplying a variable value represented by modulation of a first carrier wave continuously by said second variable represented byan angle and expressing the product as a modulation of a similar carrier wave, the combination of a source of said first carrier wave, means for modulating said carrier wave in accordance with the magnitude of said variable value, an induction member connected to said source for creating a magnetic field in response to said first modulated carrier wave, a second induction member positioned in said magnetic field, means for adjusting said second induction member through said angle, series connections between said first and second induction members, a third induction I member in the field of said second induction member and responsive only to a function of the magnetic fields created by said first and second induction members, and an indicator energized by the voltage induced in said third member for indicating said multiplication, the turn ratio between said second and first induction members being .28 or 3.57.

' GEORGE AGINS.

REFERENCES crrEn The following references are'o! record in the file of this patent:

UNITED STATES PATENTS Alexanderson "L--- Mar. 11, 1947 

